Question

пожалуйста помогите с контрольной умоляю даю 40 балов ​

Answer 1

Ответ:

Объяснение:

№1

$\[\begin{cases} 2x+3 > x \\4x > x+3\end{cases}\\\\\\\begin{cases} 2x-x > -3 \\4x-x > 3\end{cases}\\\\\\\begin{cases} x > -3 \\3x > 3\end{cases}\\\\\\\begin{cases} x > -3 \\x > 1\end{cases}\\\\\downarrow \qquad \downarrow\\\\\boxed{x > 1}\]$

Ответ: $\begin{align} 2x + y &= 8 \\ 3x - 2y &= 1\end{align}$2

№2

$\[\begin{cases} x\leq 3 \\x < 5\end{cases}\\\\\downarrow \qquad \downarrow \\\\\boxed {x\leq 3}\]$

№3

$a)$

    $\[\begin{cases} 5x+4\geq 2 \\3-2x < 4\end{cases}\\\\\\\begin{cases} 5x\geq 2 -4 \\2x > 3-4\end{cases}\\\\\\\begin{cases} 5x\geq -2 \\2x > -1\end{cases}\\\\\\\begin{cases} x\geq -\frac{2}{5} \\x > -\frac{1}{2} \end{cases}\\\\ \downarrow \qquad \quad \downarrow \\\\\boxed{x\geq -\frac{2}{5} }\]$

$b)$

    $\[\begin{cases} 6x(x-1)-3x(2x-1) < x \\0,5x-3,7 < 0,3x-0,7\end{cases}\\\\\\\begin{cases} 6x^2-6x-6x^2+3x < x \\0,5x-0,3x < -0,7+3,7\end{cases}\\\\\\\begin{cases} -3x-x < 0 \\0,2x < 3\end{cases}\\\\\\\begin{cases} 4x > 0 \\x < 3:0,2\end{cases}\\\\\\\begin{cases} x > 0 \\x < 15\\\end{cases}\\\\\downarrow \qquad \downarrow \qquad \downarrow\\\\\boxed{x \in (0; \ 5)}\]$

№4

$\dfrac{x-3}{x+2}\leq 0$

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ОДЗ:  $x+2\neq 0$

           $x\neq -2$

==================================

$\\\\\[\begin{cases} x - 3 \leq 0 \\ x + 2 > 0\end{cases}\quad or \qquad\begin{cases} x - 3 \geq 0 \\ x + 2 < 0\end{cases}\\\\\\\begin{cases} x \leq 3 \\ x > -2\end{cases}\quad or \qquad\begin{cases} x \geq 3 \\ x < -2\end{cases}\\\\\downarrow \qquad \downarrow \qquad \downarrow\\\\\boxed{x\in (-2; \ 3] }\]$

№5

$-2\leq \dfrac{3x+1}{8}\leq 0\\\\\\\dfrac{-2\times8}{8}\leq \dfrac{3x+1}{8}\leq \dfrac{0 \times 8}{8} \\\\\\-16\leq 3x+1\leq 0\\\\\\-16-1\leq 3x\leq 0-1\\\\\\-17\leq 3x\leq -1\\\\\\-\dfrac{17}{3} \leq \dfrac{3x}{3} \leq -\dfrac{1}{3} \\\\\\-\dfrac{17}{3} \leq x\leq -\dfrac{1}{3} \\\\\\\boxed{x \in \left[-\frac{17}{3} ; \ -\frac{1}{3} \right] }$